Cover with vinegar-soaked paper towels and keeping the paper towels soaked with white vinegar, leave on the hard water spots and rust stains for an hour or so. Remove the towels and then scrub with a dampened plastic scrubber sprinkled with a little baking soda. Repeat if necessary.
To remove rust stains from clothing, moisten spot with lemon juice, sprinkle with salt and expose to sunlight. To remove rust stains from white washables, cover the stains with cream of tartar, gather up the ends of the article so that the powder stays on the spot, dip the whole thing in hot water for 5 minutes, then wash as usual.
I'm not sure if these methods will work on things other then clothing.. let me know if you've tried that with success...